# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\lim_{x\to-4}\left(\frac{x+4}{\sqrt{3x+13}-1}\right)$

Learn how to solve limits by factoring problems step by step online.

$\lim_{x\to-4}\left(\frac{x+4}{\sqrt{3x+13}-1}\frac{\sqrt{3x+13}+1}{\sqrt{3x+13}+1}\right)$

Learn how to solve limits by factoring problems step by step online. Evaluate the limit of (x+4)/((3x+13)^0.5-1) as x approaches -4. Applying rationalisation. Multiplying fractions. Solve the product of difference of squares \left(\sqrt{3x+13}-1\right)\left(\sqrt{3x+13}+1\right). Factor by the greatest common divisor 3.

$\frac{2}{3}$$\,\,\left(\approx 0.6666666666666666\right)$

### Problem Analysis

$\lim_{x\to-4}\left(\frac{x+4}{\sqrt{3x+13}-1}\right)$

### Main topic:

Limits by factoring

~ 0.07 seconds